The standard model of online prediction deals with serial processing of inputs by a single processor. However, in large-scale online prediction problems, where inputs arrive at a high rate, an increasingly common necessity is to distribute the computation across several processors. A non-trivial challenge is to design distributed algorithms for online prediction, which maintain good regret guarantees. In \cite{DMB}, we presented the DMB algorithm, which is a generic framework to convert any serial gradient-based online prediction algorithm into a distributed algorithm. Moreover, its regret guarantee is asymptotically optimal for smooth convex loss functions and stochastic inputs. On the flip side, it is fragile to many types of failures that are common in distributed environments. In this companion paper, we present variants of the DMB algorithm, which are resilient to many types of network failures, and tolerant to varying performance of the computing nodes.
Tongji University（同济大学）；Shanghai Research Institute for Intelligent Autonomous Systems（上海智能自主系统研究院）；Nanyang Technological University（南洋理工大学）；Harvard University（哈佛大学）
Distributed online optimization and game have been increasingly researched in the last decade, mostly motivated by its wide applications in sensor networks, robotics (e.g., distributed target tracking and formation control), smart grids, deep learning, and so forth. In these problems, there is a network of agents who may be cooperative (i.e., distributed online optimization) or noncooperative (i.e., online game) through local information exchanges. And the local cost function of each agent is often time-varying in dynamic and even adversarial environments. At each time, a decision must be made…
Distributed Online Convex Optimization with Nonseparable Costs and Constraints
Department of Systems Engineering, City University of Hong Kong（系统工程系，香港城市大学）；Department of Electrical and Computer Engineering, New York University（电气计算机工程系，纽约大学）；Department of Civil and Urban Engineering, New York University（土木与城市工程系，纽约大学）；Department of Civil Engineering Technology and Environmental Management Safety, Rochester Institute of Technology（土木工程科技与环境管理安全系，罗切斯特理工学院）
KTH Royal Institute of Technology（瑞典皇家理工学院）；Digital Futures（数字未来）；Tongji University（同济大学）；Shanghai Research Institute for Intelligent Autonomous Systems（上海自主智能无人系统科学中心）；Northeastern University（东北大学）；Nanyang Technological University（南洋理工大学）
This paper considers the distributed online convex optimization problem with time-varying constraints over a network of agents. This is a sequential decision making problem with two sequences of arbitrarily varying convex loss and constraint functions. At each round, each agent selects a decision from the decision set, and then only a portion of the loss function and a coordinate block of the constraint function at this round are privately revealed to this agent. The goal of the network is to minimize the network-wide loss accumulated over time. Two distributed online algorithms with full-info…
Classical linear quadratic (LQ) control centers around linear time-invariant (LTI) systems, where the control-state pairs introduce a quadratic cost with time-invariant parameters. Recent advancement in online optimization and control has provided novel tools to study LQ problems that are robust to time-varying cost parameters. Inspired by this line of research, we study the distributed online LQ problem for identical LTI systems. Consider a multi-agent network where each agent is modeled as an LTI system. The LTI systems are associated with decoupled, time-varying quadratic costs that are rev…
University of Southern California（南加州大学）；Hanyang University（汉阳大学）
We consider the problem of learning a nonlinear function over a network of learners in a fully decentralized fashion. Online learning is additionally assumed, where every learner receives continuous streaming data locally. This learning model is called a fully distributed online learning (or a fully decentralized online federated learning). For this model, we propose a novel learning framework with multiple kernels, which is named DOMKL. The proposed DOMKL is devised by harnessing the principles of an online alternating direction method of multipliers and a distributed Hedge algorithm. We theo…
Online optimization has recently opened avenues to study optimal control for time-varying cost functions that are unknown in advance. Inspired by this line of research, we study the distributed online linear quadratic regulator (LQR) problem for linear time-invariant (LTI) systems with unknown dynamics. Consider a multi-agent network where each agent is modeled as a LTI system. The network has a global time-varying quadratic cost, which may evolve adversarially and is only partially observed by each agent sequentially. The goal of the network is to collectively (i) estimate the unknown dynamic…
University of Pennsylvania（宾夕法尼亚大学）；University of California, Berkeley（加州大学伯克利分校）
Graph neural networks (GNNs) learn representations from network data with naturally distributed architectures, rendering them well-suited candidates for decentralized learning. Oftentimes, this decentralized graph support changes with time due to link failures or topology variations. These changes create a mismatch between the graphs on which GNNs were trained and the ones on which they are tested. Online learning can be used to retrain GNNs at testing time, overcoming this issue. However, most online algorithms are centralized and work on convex problems (which GNNs rarely lead to). This pape…
Johnson Controls（江森自控）；Iowa State University（爱荷华州立大学）；New York University（纽约大学）
Regret has been widely adopted as the metric of choice for evaluating the performance of online optimization algorithms for distributed, multi-agent systems. However, data/model variations associated with agents can significantly impact decisions and requires consensus among agents. Moreover, most existing works have focused on developing approaches for (either strongly or non-strongly) convex losses, and very few results have been obtained regarding regret bounds in distributed online optimization for general non-convex losses. To address these two issues, we propose a novel composite regret …
Graph Neural Network-Based Distributed Optimal Control for Linear Networked Systems: An Online Distributed Training Approach
Department of Electrical Engineering, University of Notre Dame（电气工程系，诺丁汉大学）；Department of Electrical and Computer Engineering, Stevens Institute of Technology（电气与计算机工程系，史蒂文斯理工学院）
This paper addresses safe distributed online optimization over an unknown set of linear safety constraints. A network of agents aims at jointly minimizing a global, time-varying function, which is only partially observable to each individual agent. Therefore, agents must engage in local communications to generate a safe sequence of actions competitive with the best minimizer sequence in hindsight, and the gap between the two sequences is quantified via dynamic regret. We propose distributed safe online gradient descent (D-Safe-OGD) with an exploration phase, where all agents estimate the const…
Graph neural networks (GNNs) are naturally distributed architectures for learning representations from network data. This renders them suitable candidates for decentralized tasks. In these scenarios, the underlying graph often changes with time due to link failures or topology variations, creating a mismatch between the graphs on which GNNs were trained and the ones on which they are tested. Online learning can be leveraged to retrain GNNs at testing time to overcome this issue. However, most online algorithms are centralized and usually offer guarantees only on convex problems, which GNNs rar…
We study robust mean estimation in an online and distributed scenario in the presence of adversarial data attacks. At each time step, each agent in a network receives a potentially corrupted data point, where the data points were originally independent and identically distributed samples of a random variable. We propose online and distributed algorithms for all agents to asymptotically estimate the mean. We provide the error-bound and the convergence properties of the estimates to the true mean under our algorithms. Based on the network topology, we further evaluate each agent's trade-off in c…
Identification of linear time-invariant (LTI) systems plays an important role in control and reinforcement learning. Both asymptotic and finite-time offline system identification are well-studied in the literature. For online system identification, the idea of stochastic-gradient descent with reverse experience replay (SGD-RER) was recently proposed, where the data sequence is stored in several buffers and the stochastic-gradient descent (SGD) update performs backward in each buffer to break the time dependency between data points. Inspired by this work, we study distributed online system iden…
We study the problem of non-constrained, discrete-time, online distributed optimization in a multi-agent system where some of the agents do not follow the prescribed update rule either due to failures or malicious intentions. None of the agents have prior information about the identities of the faulty agents and any agent can communicate only with its immediate neighbours. At each time step, a locally Lipschitz strongly convex cost function is revealed locally to all the agents and the non-faulty agents update their states using their local information and the information obtained from their n…
University of Southern California（南加州大学）；Hanyang University（汉阳大学）
In the Internet-of-Things (IoT) systems, there are plenty of informative data provided by a massive number of IoT devices (e.g., sensors). Learning a function from such data is of great interest in machine learning tasks for IoT systems. Focusing on streaming (or sequential) data, we present a privacy-preserving distributed online learning framework with multiplekernels (named DOMKL). The proposed DOMKL is devised by leveraging the principles of an online alternating direction of multipliers (OADMM) and a distributed Hedge algorithm. We theoretically prove that DOMKL over T time slots can achi…
Distributed Associative Memory via Online Convex Optimization
KCLIP, CIIPS, Department of Engineering, King’s College London, London WC2R 2LS, UK（KCLIP、CIIPS、工程系、伦敦国王学院，伦敦 WC2R 2LS，英国）；Communication Systems Department, EURECOM, 06904 Sophia Antipolis, France（通信系统部门、EURECOM、法国索菲亚抗皮斯，06904）；Intelligent Networked Systems Institute, Northeastern University London, London E1 8PH, UK（智能网络系统研究所、伦敦东北大学、伦敦 E1 8PH，英国）
We study the problem of estimating an unknown parameter in a distributed and online manner. Existing work on distributed online learning typically either focuses on asymptotic analysis, or provides bounds on regret. However, these results may not directly translate into bounds on the error of the learned model after a finite number of time-steps. In this paper, we propose a distributed online estimation algorithm which enables each agent in a network to improve its estimation accuracy by communicating with neighbors. We provide non-asymptotic bounds on the estimation error, leveraging the stat…
Distributed Autonomous Online Learning: Regrets and Intrinsic Privacy-Preserving Properties
Purdue University（普渡大学）；University of Waterloo（滑铁卢大学）
在线学习在处理海量数据方面越来越受欢迎。然而，在线学习的顺序性质需要集中式学习器来存储数据和更新参数。在本文中，我们考虑在线学习与{ \em分布式}数据源。自主学习器根据本地数据源更新本地参数，并定期与通信网络中的一小部分邻居交换信息。我们推导了强凸函数的遗憾界，推广了Ram et al.（2010）关于凸函数的工作。最重要的是，我们表明，我们的算法具有\emph{intrinsic}隐私保护属性，我们证明了隐私保护的充分必要条件在网络中。这些条件意味着，对于具有大于一的连通性的网络，恶意学习者无法重建其他学习者的子梯度（和敏感的原始数据），这使得我们的算法在隐私敏感的应用程序中具有吸引力。
Distributed Private Online Learning for Social Big Data Computing over Data Center Networks
Huazhong University of Science & Technology（华中科技大学）；Peking University（北京大学）；Northwestern Polytechnical University（西北工业大学）；National University of Singapore（新加坡国立大学）
William & Mary（威廉与玛丽学院）；Old Dominion University（欧道明大学）
As the number of IoT devices has increased rapidly, IoT botnets have exploited the vulnerabilities of IoT devices. However, it is still challenging to detect the initial intrusion on IoT devices prior to massive attacks. Recent studies have utilized power side-channel information to identify this intrusion behavior on IoT devices but still lack accurate models in real-time for ubiquitous botnet detection. We proposed the first online intrusion detection system called DeepAuditor for IoT devices via power auditing. To develop the real-time system, we proposed a lightweight power auditing device…
Distributed Online Convex Optimization with Compressed Communication: Optimal Regret and Applications
National Key Laboratory for Novel Software Technology, Nanjing University（南京大学计算机软件新技术国家重点实验室）；School of Artificial Intelligence, Nanjing University（南京大学人工智能学院）
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Princeton University（普林斯顿大学）；Massachusetts Institute of Technology（麻省理工学院）
We consider a distributed reinforcement learning setting where multiple agents separately explore the environment and communicate their experiences through a central server. However, $α$-fraction of agents are adversarial and can report arbitrary fake information. Critically, these adversarial agents can collude and their fake data can be of any sizes. We desire to robustly identify a near-optimal policy for the underlying Markov decision process in the presence of these adversarial agents. Our main technical contribution is Weighted-Clique, a novel algorithm for the robust mean estimation fro…
University of Toronto（多伦多大学）；Wayne State University（韦恩州立大学）
Distributed optimization is vital in solving large-scale machine learning problems. A widely-shared feature of distributed optimization techniques is the requirement that all nodes complete their assigned tasks in each computational epoch before the system can proceed to the next epoch. In such settings, slow nodes, called stragglers, can greatly slow progress. To mitigate the impact of stragglers, we propose an online distributed optimization method called Anytime Minibatch. In this approach, all nodes are given a fixed time to compute the gradients of as many data samples as possible. The re…
